We show that strong duality for conic linear programming directly implies the minimax theorem for a wide class of infinite two-player zero-sum games. In fact, for every two-player zero-sum game with "cone-leveled" strategy sets, or more generally with strategy sets that can be written as unions of "cone-leveled" subsets, its game value and (approximate) optimal strategies can be calculated by solving a primal-dual pair of conic linear problems. The original result proven by von Neumann is therefore naturally generalized to the infinite-dimensional case, and a strong, rigorous connection between infinite two-player zero-sum games and mathematical programming is established.

翻译：我们证明锥线性规划的强对偶性直接蕴含了一类广泛无限两人零和博弈的极小化极大定理。事实上，对于具有"锥分层"策略集，或更一般地策略集可表示为"锥分层"子集之并的每个两人零和博弈，其博弈值与（近似）最优策略均可通过求解一对原-对偶锥线性问题来计算。冯·诺依曼证明的原始结果因此自然推广至无限维情形，并在无限两人零和博弈与数学规划之间建立了严谨的强关联。